Invariant character recognition with Zernike and orthogonal Fourier-Mellin moments

In this paper, we consider the use of orthogonal moments for invariant classification of alphanumeric characters of different size. In addition to the Zernike and pseudo-Zernike moments (ZMs and PZMs) which have been previously proposed for invariant character recognition, a new method of combining Orthogonal Fourier-Mellin moments (OFMMs) with centroid bounding circle scaling is introduced, which is shown to be useful in characterizing images with large variability. Through extensive experimentation using ZMs and OFMMs as features, different scaling methodologies and classifiers, it is shown that OFMMs give the best overall performance in terms of both image reconstruction and classification accuracy.     

An efficient and robust multi-frame image super-resolution reconstruction using orthogonal Fourier-Mellin moments

Multi-frame image super-resolution (SR) has recently become an active area of research. The orthogonal rotation invariant moments (ORIMs) have several useful characteristics which make them very suitable for multi-frame image super-resolution application. Among the various ORIMs, Zernike moments (ZMs) and pseudo-Zernike moments (PZMs)-based SR approaches, i.e., NLM-ZMs and NLM-PZMs, have already shown improved SR performances for multi-frame image super-resolution. However, it is a well-known fact that among many ORIMs, orthogonal Fourier-Mellin moments (OFMMs) demonstrate better noise robustness and image representation capabilities for small images as compared to ZMs and PZMs. Therefore, in this paper, we propose a multi-frame image super-resolution approach using OFMMs. The proposed approach is based on the NLM framework because of its inherent capability of estimating motion implicitly. We have referred to this proposed approach as NLM-OFMMs-I. Also, a novel idea of using OFMMs-based interpolation in place of traditional Lanczos interpolation for obtaining an initial estimate of HR sequence has been presented in this paper. This variant of the proposed approach is referred to as NLM-OFMMs-II. Detailed experimental analysis demonstrates the effectiveness of the proposed OFMMs-based SR approaches to generate high-quality HR images in the presence of factors like image noise, global motion, local motion, and rotation in between the image frames.     

A high capacity image adaptive watermarking scheme with radial harmonic Fourier moments

In this paper, we introduce a novel image adaptive technique for high capacity watermarking scheme using accurate and fast radial harmonic Fourier moments (RHFMs). The high embedding capacity is achieved by improving the hiding ratio after reducing inaccuracies in the computation of RHFMs. The binary watermark is embedded by performing the conditional quantization of selected RHFMs magnitudes to minimize the spatial distortion added to the host image. In addition, fast algorithms based on 8-way symmetry/anti-symmetry properties and recursive relations for the computation of sinusoidal kernel functions are adopted to enhance the speed of RHFMs-based watermarking process. Experimental studies show that the proposed watermarking scheme provides higher embedding capacity, good visual imperceptibility, better robustness to geometric distortions and common signal processing transformations, and lower computational complexity compared to the existing Zernike and pseudo-Zernike moments (ZMs/PZMs)-based watermarking schemes.     

A novel algorithm for fast computation of Zernike moments

Zernike moments (ZMs) have been successfully used in pattern recognition and image analysis due to their good properties of orthogonality and rotation invariance. However, their computation by a direct method is too expensive, which limits the application of ZMs. In this paper, we present a novel algorithm for fast computation of Zernike moments. By using the recursive property of Zernike polynomials, the inter-relationship of the Zernike moments can be established. As a result, the Zernike moment of order n with repetition m, Z_nm, can be expressed as a combination of Z_n−2,m and Z_n−4,m. Based on this relationship, the Zernike moment Z_nm, for n>m, can be deduced from Z_mm. To reduce the computational complexity, we adopt an algorithm known as systolic array for computing these latter moments. Using such a strategy, the multiplication number required in the moment calculation of Z_mm can be decreased significantly. Comparison with known methods shows that our algorithm is as accurate as the existing methods, but is more efficient.     

Fast and numerically stable methods for the computation of Zernike moments

Zernike moments (ZMs) are used in many image processing applications due to their superior performance over other moments. However, they suffer from high computation cost and numerical instability at high order of moments. In the past many recursive methods have been developed to improve their speed performance and considerable success has been achieved. The analysis of numerical stability has also gained momentum as it affects the accuracy of moments and their invariance property. There are three recursive methods which are normally used in ZMs calculation—Prata’s, Kintner’s and q-recursive methods. The earlier studies have found the q-recursive method outperforming the two other methods. In this paper, we modify Prata’s method and present a recursive relation which is proved to be faster than the q-recursive method. Numerical instability is observed at high orders of moments with the q-recursive method suffering from the underflow problem while the modified Prata’s method suffering from finite precision error. The modified Kintner’s method is the least susceptible to these errors. Keeping in view the better numerical stability, we further make the modified Kintner’s method marginally faster than the q-recursive method. We recommend the modified Prata’s method for low orders (≤90) and Kintner’s fast method for high orders (>90) of ZMs.     

On invariance analysis of Zernike moments in the presence of rotation with crop and loose modes

Zernike moments are widely applied in digital image processing fields based on many desirable properties, such as rotational invariance, noise robust and efficient representation of pattern. On the computational analysis of Zernike moment is challenging issue. From an algorithmic aspect, in this paper we investigate the effect of image rotation (including crop rotation and loose rotation) operations on Zernike moments in both theoretical and experimental ways. For the crop rotation, we suggest to extract the Zernike moments by mapping the image over a disc instead of inside a circle since the outside of an image after the crop rotation will be distorted. Referring to the loose rotation, we propose a preprocessing step (which is called image size normalization) to embed an image and its rotated versions into a predefined size of zero-value image in such a way that the effect of image size change due to loose rotation can be eliminated. By incorporating the proposed image size normalization operation, we introduce an effective extraction method of image Zernike moments against loose rotation operation. Experimental results show the validity of the proposed extraction method.     

The new HCI? navigation of information space

When we use the term ‘human–computer interaction’ (HCI), the image that is conjured up is of a person sitting at a visual display unit staring in at the world of ‘information’; the person is very much outside the space of information. But when we think of other activities such as going shopping, having a meeting or driving across town, we do not think of the person as outside this space. On the contrary, we see the person as inside a space of activities, surrounded by, and interacting with, assorted artefacts and people. Navigation of Information Space is an alternative conceptualisation of HCI that sees people as existing inside information spaces. Looking at HCI in this way means looking at HCI design as the creation of information spaces. This paper explores these ideas in more detail, arguing that Navigation of Information Space is not just a metaphor for HCI; it is a ‘paradigm shift’. The paper illustrates how Semiotics has informed this conception and discusses why such a paradigm shift is needed.     

Representation of an alpine treeline ecotone in SPOT 5 HRG data

An ecotone is a zone of vegetation transition between two communities, often resulting from a natural or anthropogenic environmental gradient. In remotely sensed imagery, an ecotone may appear as an edge, a boundary of mixed pixels or a zone of continuous variation, depending on the spatial scale of the vegetation communities and their transition zone in relation to the spatial resolution of the imagery. Often in image classification, an ecotone is either ignored if it falls within a width of one or two pixels, or part of it may be mapped as a separate vegetation community if it covers an area of several pixel widths. A soft classification method, such as probability mapping, is inherently appealing for mapping vegetation transition. Ideally, the probability of membership each pixel has to each vegetation class corresponds with the proportional composition of vegetation classes per pixel. In this paper we investigate the use of class probability mapping to produce a softened classification of an alpine treeline ecotone in Austria using a SPOT 5 HRG image. Here the transition with altitude is from dense subalpine forest to treeless alpine meadow and herbaceous vegetation. The posterior probabilities from a Maximum Likelihood algorithm are shown to reflect the land-cover composition of mixed pixels in the ecotone. The relationships between the posterior probability of class membership for the two end-member classes of ‘scrub and forest’ and ‘non-forest vegetation’ and the percentage ground cover of these vegetation classes (enumerated in 15 quadrats from 1:1500 aerial photographs) were highly significant: r² = 0.83 and r² = 0.85 respectively (p < 0.001, n = 15). We identify thresholds (alpha-cuts) in the posterior probabilities of class membership of ‘scrub and forest’ and ‘non-forest vegetation’ to map the alpine treeline ecotone as a transition zone of five intermediate vegetation classes between the end-member communities. In addition, we investigate the representation of the ecotone as a ratio between the posterior probabilities of ‘scrub and forest’ and ‘non-forest vegetation’. This displays the vegetation transition without imposing subjective boundaries, and has greater emphasis on the ecotone transition rather than on the end-member communities. We comment on the fitness for purpose of the different ways investigated for representing the alpine treeline ecotone.     

基于Zernike矩的视频对象零水印算法

针对几何攻击所导致的水印不同步问题,提出了一种结合Zernike矩和图像归一化的有效视频对象水印算法。Zernike矩的幅度具有旋转不变性,缩放和平移不变性通过图像归一化取得。水印嵌入采用零水印方案,解决了基于Zernike矩的图像重构效果不理想和重构过程中复杂度高的问题。实验结果表明,该水印算法对旋转、缩放等几何操作具有鲁棒性,同时对压缩、滤波、高斯噪声等常见的图像处理操作也具有鲁棒性。     

A Hamiltonian, explicit algorithm with spectral accuracy for the ‘good’ Boussinesq system

We construct an explicit pseudo-spectral method for the numerical solution of the soliton-producing ‘good’ Boussinesq system w_t = u_xxx + u_x + (u²)_x, u_t = w_x. The new scheme preserves a discrete Poisson structure similar to that of the continuous system. The scheme is shown to converge with spectral spatial accuracy. A numerical illustration is given.     

新形式勒让德矩的研究

针对传统非正交矩很难进行图像重建的缺点,以及离散矩用于重建需要重复采样的缺陷,以降低图像重建误差为目标,提出了一种以在离散坐标空间内拟合克罗内克狄拉克函数为核心思想的新形式矩的定义--基于勒让德多项式的矩,并对其性质进行了阐述。这种矩在函数空间非正交却拥有优秀的重建效果,且其在矩计算误差、旋转不变性等多个维度较目前主流矩都具有更优秀性能,特别是在目前主流图像矩表现不尽如人意的大尺寸图像领域。此外,突破性地发掘图像矩的抗噪音性能并加入性能对比。通过与目前主流的三种矩：Zernike矩、Polar-Fourier矩以及Polar Harmonic Transform（PHT）矩的对比实验,证明利用这种基于新思想的矩提取图像特征可以具有更小的信息冗余度及多个维度的鲁棒性,其在旋转不变性、减小图像重建误差以及提高抗噪稳定性方面的性能表现至少可以提高22%。     

Image analysis by Bessel-Fourier moments

In this paper, we proposed a new set of moments based on the Bessel function of the first kind, named Bessel-Fourier moments (BFMs), which are more suitable than orthogonal Fourier-Mellin and Zernike moments for image analysis and rotation invariant pattern recognition. Compared with orthogonal Fourier-Mellin and Zernike polynomials of the same degree, the new orthogonal radial polynomials have more zeros, and these zeros are more evenly distributed. The Bessel-Fourier moments can be thought of as generalized orthogonalized complex moments. Theoretical and experimental results show that the Bessel-Fourier moments perform better than the orthogonal Fourier-Mellin and Zernike moments (OFMMs and ZMs) in terms of image reconstruction capability and invariant recognition accuracy in noise-free, noisy and smooth distortion conditions.     

Emergent intelligent properties of progressively structured pattern recognition nets

The n-tuple recognition net is seen as a building brick of a progression of network structures. The emergent ‘intelligent’ properties of such systems are discussed. They include the amplification of confidence for the recognition of images that differ in small detail, a short term memory of the last seen image, sequence sensitivity, sequence acceptance and saccadic inspection as an aid in scene analysis.     

Spatially referenced methods of processing raster and vector data

The authors consider a general method of constructing addressing and arithmetic systems for two-dimensional image data using the hierarchy of ‘molecular’ tilings based on an original isohedral ‘atomic’ tiling. (Each molecular title at level k is formed from a constant number of tiles at level k−1; this is termed the ‘aperture’ property of the hierarchy.) In addition they present 11 objective criteria (which are of significance in cartographic image processing), by which these hierarchies and tilings may be described and compared.

Of the 11 topologically distinct types of isohedral tiling, three ([3⁶], [4⁴] and [6³]) are composed of regular polygons, and two of these ([3⁶] and[4⁴]) satisfy the condition that all tiles have the same ‘orientation’. In general, although each level in a hierarchy is topologically equivalent, the tiles may differ in shape at different levels and only [6³], [4⁴], [4.8²] and [4.6.12] are capable of giving rise to hierarchies in which the tiles at all levels are the same shape. The possible apertures of hierarchies obeying this condition are n² (for any n > 1)in the cases of [6³] and [4⁴]; n² or 2n² in the case of [4.8²]; and n² or 3n² in the case of [4.6.12].

In contrast the only tiling exhibiting the uniform ‘adjacency’ criterion is[3⁶]. However, hierarchies based on this atomic tiling generate molecular tiles with different shapes at every level. If these disadvantages are accepted, hierarchies based on first-level molecular tiles referred to as the 4-shape, 4′-shape, 7-shape and 9-shape are generated. Of these the 4-shape and the 9-shape appear to satisfy many of the cartographically desirable properties in addition to having an atomic tiling which exhibits uniform adjacency.

In recent years the generalized balanced ternary addressing system has been developed to exploit the image processing power of the 7-shape. The authors have generalized and extended this system as ‘tesseral addressing and arithmetic’, showing how it can be used to render a 4-shape into a spatially correct linear quadtree.     

伪Zernike矩不变性分析及其改进研究

伪 Zernike矩是基于图象整个区域的形状描述算子 ,而基于轮廓的形状描述子 ,例如曲率描述子、傅立叶描述子和链码描述子等是不能正确描述由几个不连接区域组成的形状的 ,因为这些算子只能描述单个的轮廓形状 .同时 ,由于伪 Zernike矩的基是正交径向多项式 ,和 Hu矩相比 ,除了具有旋转不变性、高阶矩和低阶矩能表达不同信息等特征外 ,还具有冗余性小、可以任意构造高阶矩等特点 ,另外 ,伪 Zernike矩还可以用于目标重构 .目前 ,伪 Zernike矩没有得到广泛的应用 ,其中的一个主要原因是 ,它不具备真正意义上的比例不变性 .为了能使伪Zernike矩得到更广泛的应用 ,在详细分析伪 Zernike矩不变性的基础上 ,提出了伪 Zernike矩的改进方法 ,使改进后的伪 Zernike矩在保持旋转不变性的同时 ,还具有真正意义上的比例不变性 ,同时给出了部分的实验分析结果 .实验结果证明 ,该改进后的伪 Zernike矩较改进前的伪 Zernike矩 ,具有更好的旋转和比例不变性 .     

Real-time integrated model for visual perception and fuzzy control

Current state-of-the-art security systems incorporate ‘passive’ and/or ‘human’ elements, the effectiveness of which can only be measured by their ability to ‘deter’ intruders. However, rapidly changing economic and cultural conditions have weakened the strengths associated with such systems. In the not too distant future, the need for an ‘active’ security system will become necessary in order to reduce the onslaught of crime.

This paper presents a conceptual basis for the incorporation of artificial intelligence concepts in the design and implementation of ‘active’ security systems. Specifically, the paper discusses issues pertaining to a real-time model for visual perception and tracking of possible intruders.